As commented in [1]}, the challenging aspects of the incompressible fluid equations lie in the constraint that the velocity should remain divergence free.
In order to preserve this divergence constraint as the domain moves, we use a different pullback map than is typically considered.
As a consequence, many of the necessary assumptions from [2]} need to be verified.
In addition, we consider a different pivot space from the typical whole \(L^2\)  space, this means that are some technical challenges which need to be addressed.
